The term “fin stacking” refers to an action of receiving a fin, which is conveyed from a press machine, through penetration of stacking pins into the fin to stack the fins. The fin stacking is summarized herebelow. A fin having been delivered from a press machine moves on a suction plate, which has a plurality of holes formed therein, while being sucked by the suction plate. After the movement of the fin, the suction plate moves up and down. Along with the up and down movement of the suction plate, the fin is cut by a cutter arranged near an outlet of the press machine, and the fin falls. The fallen fin is received with so-called stacking pins which are bars each having a needle-shaped tip, and fins are sequentially stacked. In a related-art fin stacking apparatus, a fin is moved by a plate, which has a plurality of holes formed therein and is configured to suck the fin (for example, see Patent Literature 1).